mlsanityData to 7 Oct 2026

A Multi-Modal Neural Geometric Solver with Textual Clauses Parsed from Diagram

arXiv 2302.11097 ↗First posted 22 Feb 2023cs.AI cs.CVcited by 55

On the map: LLM reasoning → Spatial and embodied reasoning

Abstract (arXiv)

Geometry problem solving (GPS) is a high-level mathematical reasoning requiring the capacities of multi-modal fusion and geometric knowledge application. Recently, neural solvers have shown great potential in GPS but still be short in diagram presentation and modal fusion. In this work, we convert diagrams into basic textual clauses to describe diagram features effectively, and propose a new neural solver called PGPSNet to fuse multi-modal information efficiently. Combining structural and semantic pre-training, data augmentation and self-limited decoding, PGPSNet is endowed with rich knowledge of geometry theorems and geometric representation, and therefore promotes geometric understanding and reasoning. In addition, to facilitate the research of GPS, we build a new large-scale and fine-annotated GPS dataset named PGPS9K, labeled with both fine-grained diagram annotation and interpretable solution program. Experiments on PGPS9K and an existing dataset Geometry3K validate the superiority of our method over the state-of-the-art neural solvers. Our code, dataset and appendix material are available at urlhttps://github.com/mingliangzhang2018/PGPS.

Key facts. Cited by 55 papers in the map (data through 7 Oct 2026). Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning. Builds on 30 of its 46 references that are in the map. First posted on arXiv 22 Feb 2023.

Builds on

30 of 46 references.

Closest ancestors · 1

Same direction, newest first

  1. 2022UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression6 Dec

Other references · 29

  1. 2017Attention Is All You Needcited by 59,932
  2. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  3. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,204
  4. 2020Language Models are Few-Shot Learnerscited by 32,199
  5. 2019BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehensioncited by 5,874
  6. 2014Neural Machine Translation by Jointly Learning to Align and Translatecited by 4,530
  7. 2014Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translationcited by 4,016
  8. 2017Bottom-Up and Top-Down Attention for Image Captioning and Visual Question Answeringcited by 1,310
  9. 2021ViLT: Vision-and-Language Transformer Without Convolution or Region Supervisioncited by 1,224
  10. 2021Are NLP Models really able to Solve Simple Math Word Problems?cited by 861
  11. 2019MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalismscited by 653
  12. 2019LayoutLM: Pre-training of Text and Layout for Document Image Understandingcited by 549
17 more
  1. 2020UnifiedQA: Crossing Format Boundaries With a Single QA Systemcited by 475
  2. 2021Unifying Vision-and-Language Tasks via Text Generationcited by 411
  3. 2021TAT-QA: A Question Answering Benchmark on a Hybrid of Tabular and Textual Content in Financecited by 402
  4. 2021Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoningcited by 376
  5. 2022Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoningcited by 347
  6. 2019Deep Modular Co-Attention Networks for Visual Question Answeringcited by 338
  7. 2021GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoningcited by 224
  8. 2020Deep Learning Based Text Classification: A Comprehensive Reviewcited by 140
  9. 2022A Survey of Deep Learning for Mathematical Reasoningcited by 124
  10. 2021Document Collection Visual Question Answeringcited by 45
  11. 2018Explicit Bias Discovery in Visual Question Answering Modelscited by 42
  12. 2021MWP-BERT: Numeracy-Augmented Pre-training for Math Word Problem Solvingcited by 32
  13. 2021Seeking Patterns, Not just Memorizing Procedures: Contrastive Learning for Solving Math Word Problemscited by 30
  14. 2022Plane Geometry Diagram Parsingcited by 20
  15. 2022PGDP5K: A Diagram Parsing Dataset for Plane Geometry Problemscited by 14
  16. 2022ELASTIC: Numerical Reasoning with Adaptive Symbolic Compilercited by 14
  17. 2021Sequence to General Tree: Knowledge-Guided Geometry Word Problem Solvingcited by 11

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 5; 2024: 12; 2025: 20; 2026: 18.

55 papers.

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  1. 2025From System 1 to System 2: A Survey of Reasoning Large Language Modelscited by 319
  2. 2025A Survey on Test-Time Scaling in Large Language Models: What, How, Where, and How Well?cited by 215
  3. 2023GeomVerse: A Systematic Evaluation of Large Models for Geometric Reasoningcited by 107
  4. 2024MoVA: Adapting Mixture of Vision Experts to Multimodal Contextcited by 82
  5. 2025RedStar: Does Scaling Long-CoT Data Unlock Better Slow-Reasoning Systems?cited by 60
  6. 2024GeoEval: Benchmark for Evaluating LLMs and Multi-Modal Models on Geometry Problem-Solvingcited by 44
  7. 2024AutoGeo: Automating Geometric Image Dataset Creation for Enhanced Geometry Understandingcited by 28
  8. 2023FormalGeo: An Extensible Formalized Framework for Olympiad Geometric Problem Solvingcited by 26
  9. 2023Mathematical Language Models: A Surveycited by 24
  10. 2025GeoSense: Evaluating Identification and Application of Geometric Principles in Multimodal Reasoningcited by 24
  11. 2023LANS: A Layout-Aware Neural Solver for Plane Geometry Problemcited by 23
  12. 2024GeoX: Geometric Problem Solving Through Unified Formalized Vision-Language Pre-trainingcited by 23
38 more
  1. 2025Enhancing the Geometric Problem-Solving Ability of Multimodal LLMs via Symbolic-Neural Integrationcited by 18
  2. 2023Adapting Large Language Models for Education: Foundational Capabilities, Potentials, and Challengescited by 13
  3. 2024LLMs Are Not Intelligent Thinkers: Introducing Mathematical Topic Tree Benchmark for Comprehensive Evaluation of LLMscited by 13
  4. 2024Fuse, Reason and Verify: Geometry Problem Solving with Parsed Clauses from Diagramcited by 13
  5. 2025TrustGeoGen: Formal-Verified Data Engine for Trustworthy Multi-modal Geometric Problem Solvingcited by 13
  6. 2024Diagram Formalization Enhanced Multi-Modal Geometry Problem Solvercited by 11
  7. 2025GeoUni: A Unified Model for Generating Geometry Diagrams, Problems and Problem Solutionscited by 11
  8. 2024Learning to Solve Geometry Problems via Simulating Human Dual-Reasoning Processcited by 10
  9. 2025Pi-GPS: Enhancing Geometry Problem Solving by Unleashing the Power of Diagrammatic Informationcited by 10
  10. 2025Towards Geometry Problem Solving in the Large Model Era: A Surveycited by 8
  11. 2024FGeo-HyperGNet: Geometric Problem Solving Integrating FormalGeo Symbolic System and Hypergraph Neural Networkcited by 7
  12. 2025Do Large Language Models Truly Understand Geometric Structures?cited by 7
  13. 2025GeoLaux: A Benchmark for Evaluating MLLMs' Geometry Performance on Long-Step Problems Requiring Auxiliary Linescited by 6
  14. 2024Improving Multimodal LLMs Ability In Geometry Problem Solving, Reasoning, And Multistep Scoringcited by 5
  15. 2025GeoDANO: Geometric VLM with Domain Agnostic Vision Encodercited by 5
  16. 2024Geo-LLaVA: A Large Multi-Modal Model for Solving Geometry Math Problems with Meta In-Context Learningcited by 4
  17. 2025A Survey of Deep Learning for Geometry Problem Solvingcited by 4
  18. 2025Thinking Machines: Mathematical Reasoning in the Age of LLMscited by 4
  19. 2025GeoBench: Rethinking Multimodal Geometric Problem-Solving via Hierarchical Evaluationcited by 4
  20. 2026Milestones over Outcome: Unlocking Geometric Reasoning with Sub-Goal Verifiable Rewardcited by 4
  21. 2025Rethinking the Text-Vision Reasoning Imbalance in MLLMs through the Lens of Training Recipescited by 3
  22. 2026Socratic-Geo: Synthetic Data Generation and Geometric Reasoning via Multi-Agent Interactioncited by 2
  23. 2026Uncovering Understanding-Generation Synergy in Native Unified Multimodal Models: From Representation, Task to Systemcited by 2
  24. 2024GAPS: Geometry-Aware Problem Solvercited by 1
  25. 2025Foundation of Intelligence: Review of Math Word Problems from Human Cognition Perspectivecited by 1
  26. 2025DynaSolidGeo: A Dynamic Benchmark for Genuine Spatial Mathematical Reasoning of VLMs in Solid Geometrycited by 1
  27. 2025GeoLoom: High-quality Geometric Diagram Generation from Textual Inputcited by 1
  28. 2026GeoFocus: Blending Efficient Global-to-Local Perception for Multimodal Geometry Problem-Solvingcited by 1
  29. 2026Enhancing Geometric Perception in VLMs via Translator-Guided Reinforcement Learningcited by 1
  30. 2026GeoChallenge: A Multi-Answer Multiple-Choice Benchmark for Geometric Reasoning with Diagramscited by 1
  31. 2026Geoparsing: Diagram Parsing for Plane and Solid Geometry with a Unified Formal Languagecited by 1
  32. 2025GeoRef: Referring Expressions in Geometry via Task Formulation, Synthetic Supervision, and Reinforced MLLM-based Solutionscited by 0
  33. 2026Concise Geometric Description as a Bridge: Unleashing the Potential of LLM for Plane Geometry Problem Solvingcited by 0
  34. 2026A Survey of Multimodal Mathematical Reasoning: From Perception, Alignment to Reasoningcited by 0
  35. 2026BiNSGPS: Geometry Problem Solving via Bidirectional Neuro-Symbolic Interactioncited by 0
  36. 2026Internalizing Geometric Law: Learning from Solver Residuals for Precision-Critical Generationcited by 0
  37. 2026GeoDial: A Multimodal Conversational Tutoring Dataset for Geometry Problem-Solving with Visual Tutor Turnscited by 0
  38. 2026VeriGeo: Controllable Geometry Question Generation with Numerical and Analytical Verificationcited by 0

50 most cited of 55 All 55 (JSON)

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  1. 2025Plane Geometry Problem Solving with Multi-modal Reasoning: A Survey
  2. 2025AutoGPS: Automated Geometry Problem Solving via Multimodal Formalization and Deductive Reasoning
  3. 2026Beyond Symbolic Solving: Multi Chain-of-Thought Voting for Geometric Reasoning in Large Language Models
  4. 2026Hilbert-Geo: Solving Solid Geometric Problems by Neural-Symbolic Reasoning
  5. 2025GeoSketch: A Neural-Symbolic Approach to Geometric Multimodal Reasoning with Auxiliary Line Construction and Affine Transformation
  6. 2024GeoCoder: Solving Geometry Problems by Generating Modular Code through Vision-Language Models
  7. 2026Dense Neuro-Symbolic Reasoning in a Unified Geometry State
  8. 2025GenesisGeo: Technical Report